渐近准周期势场中电子的局域态,扩展态和迁移率边界

应用数值方法研究了一维渐近准周期势Ｖｎ＝λｃｏｓ（Ｑｎ＋αｎν）（０＜ν＜１，及为无理数）中运动的电子的能级和波函数，发现当λ＞２时，所有的态都是局域态，而当λ＜２时，存在着扩展态、局域态和迁移率边界．我们研究了它们与参数Ｑ，α，ν的关系，发现能带结构由Ｑ决定，而α，ν是无关的参数．     

在Mindlin板理论中弯板角点邻域内的本征解

本文从由Assiff和Yen引进的Mindlin板理论的向量方程组出发,求得在边界角点邻域内的渐近解,进而在各种可能的边界条件下,求得决定解参数λ的本征方程。     

二阶非线性微分方程的渐近性

利用Gronwall不等式研究了二阶非线性泛涵微分方程的非振动解及其一阶导数的有界性与渐近性 ,改进和推广一些已知文献中的相应结果 .     

双参数指数分布参数变点的统计推断

讨论双参数指数分布尺度参数发生变化、两个参数可能同时发生变化时，变点的统计推断问题。关于尺度参数变点问题，继续Wang和Bhatti(1998)的讨论，给出检验的渐近分布，同时也研究变点的估计问题。对于位置参数和尺度参数可能同时发生变化时，给出参数变点检验统计量，并利用随机模拟的方法给出检验的临界值。     

Boltzmann方程Cauchy问题的光滑解

在一些合理的物理假设下,研究了一类Boltzmann方程Cauchy问题光滑解的存在唯一性、渐近衰减性、渐近增长性及Blow-up现象,给出了整体解的渐近衰减性和渐过增长性以及局部解的破裂现象(Blow-up)的充分条件.     

热弹性梁振动系统的渐近稳定性

本文研究了热弹性梁分布参数系统,用Hilbert空间中线性算子半群理论证明了该系统的解存在且唯一,并得出了系统的稳定性结论.     

临床医学中的一类非线性反应扩散方程模型的摄动方法

本文研究了一类非线性微分方程的Michaelis-Mentn动力学模型。利用摄动方法求得了相应初值问题的渐近解。     

一类亏度为2的四次插值样条误差的渐近性态

分析了一类亏度为２的四次插值样条，给出了三种插值样条及其导函数余项的渐近展开式。     

一类三次Spline插值误差的渐近展开

对一类有广泛实用价值的无导数信息插值端点条件的三次样条函数,给出了插值误差的逐项渐近展开式。     

On the Discrepancy Measures for the Optimal Equal Probability Partitioning in Bayesian Multivariate Micro-Aggregation

Data holders, such as statistical institutions and financial organizations, have a very serious and demanding task when producing data for official and public use. It’s about controlling the risk of identity disclosure and protecting sensitive information when they communicate data-sets among themselves, to governmental agencies and to the public. One of the techniques applied is that of micro-aggregation. In a Bayesian setting, micro-aggregation can be viewed as the optimal partitioning of the original data-set based on the minimization of an appropriate measure of discrepancy, or distance, between two posterior distributions, one of which is conditional on the original data-set and the other conditional on the aggregated data-set. Assuming d-variate normal data-sets and using several measures of discrepancy, it is shown that the asymptotically optimal equal probability m-partition of , with m ^1/d ∈ , is the convex one which is provided by hypercubes whose sides are formed by hyperplanes perpendicular to the canonical axes, no matter which discrepancy measure has been used. On the basis of the above result, a method that produces a sub-optimal partition with a very small computational cost is presented. Published online xx, xx, xxxx.